Question: Rewrite as a simplified fraction. ${0.9\overline{75} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 975.7575...\\ 10x &= 9.7575...\end{align*}}$ Subtracting the two equations, we have: ${990x = 966}$ ${x = \dfrac{966}{990}} $ ${x = \dfrac{161}{165}} $